The correct answer is "some combination of the above":
- Arduino Nano is based on the ATmega168/328 chip, which does support SPI in hardware.
- The SPI library only supports hardware SPI (regardless of the Arduino model). Note that you could bitbang (relatively) slow SPI without any problems, this would be a relatively easy software implementation.
- The status of SPI library should be considered same as the status of the Wire library: not part of core Arduino services (in contrast to PWM, ADC, and digital GPIO), but widely supported nonetheless.
So perhaps the closest answer in your multiple-choice question is "out of date". The status of SPI should look the same as the status of I2C.